Solve triangle ABC shown in the following figure. (Enter all angles in degrees. Round your answers to one decimal place.)

Question

A triangle is given.

1. The angle at vertex C is 120°.
2. The side opposite vertex A has length 16.
3. The side opposite vertex B has length 11.

c=

∠A= 

∠B=

Answer 1

First, use the law if cosines to find the length of the missing side:

a² = b² + c² – 2bc cos α, where a,b, and c are the sides of triangle and α is the angle between sides b and c. 

The length of the missing side is approximately 23.52 units, or 23.5 units to one decimal place.

An alternate form of the law of cosines is:

cos A = (b² + c² - a²) / (2bc)

This form can be used to find the missing angles.

Using the formula once results in 36.11 degrees, and using it a second time, 23.9 degrees, approximately.

If you need the details, please let me know.